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Classification of shapes Tracking of morphological changes. Why describe shapes?. Results. How describe shapes ?. S’(t n+1 ). S’(t n ). Fourier Descriptors. Measurements. Invariance. Improved FD’s. Similarity. Examples. Shape analysis. Prior knowledge. S’(t n-1 ). y.
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Classification of shapes • Tracking of morphological changes Why describe shapes? Results How describeshapes? S’(tn+1) S’(tn) Fourier Descriptors Measurements Invariance Improved FD’s Similarity Examples Shape analysis Prior knowledge S’(tn-1) y An example of a transformed contour S’(t) is a different parameterisation of the contour S(0) 0 x Ghent University, Dept. Of Telecommunications and Information Processing IMPROVED FOURIER DESCRIPTORS FOR2-D SHAPE REPRESENTATION http://telin.ugent.be/ipi Jonas.DeVylder@telin.UGent.be Automatic detection of an object in an image is a difficult task. If the expected object has a certain shape, this shape information can be incorporated as a constraint in the detection algorithm. Techniques able to use this information are: • Snakes • Hough-transform • Active Shape Models • … • Retrieve similar shapes out of a database • Interpolate between two similar shapes • Use the descriptors in a metric to measure difference The FD’s can be made invariantto: • translation • Scaling • Rotation • Changing the starting point of S(t) S(t) is not a uniqueparametisation! S(tn+1) Jonas De Vylder, Wilfried Philips Approximate s(t) S(tn) y An example of a contour Improve the FD-approximation by changing the scanning speed θ(t) of the contour S(tn-1) S(t) is a parameterisation of the contour S(0) 0 x • Bn are chosen to minimize the mean squared distance between S and SN • SN can easily be calculated using the FFT • Bn are called Fourier Descriptors (FD’s) • Gn minimizes: • S*N can be calculated without interpolating S • Gn are called Improved Fourier Descriptors (IFD’s) • 436 leaf contours where approximated • The database contains 6 different families of leaves • All leaves where approximated using 10,20,…,50 (Improved) Fourier Descriptors • Two different error metrics are used to compare the FD’s and IFD’s: • A maximum distance between the original and the approximation • An average distance between the original and the approximation • For both measurements the IFD’s on average approximated over 10% better than the FD’s Jonas.devylder@telin.ugent.be 10 FD’s Original shape 10 IFD’s
